Optical coherence tomography using nonstationary signal processing based on continuous wavelet transform

Heart valve disorders, caused by congenital defects, rheumatic fever, calcification, myocardial infarction and other cardiovascular diseases, often require native valves to be replaced by bio-prosthetic devices or mechanical heart valves (MHVs). Among MHVs, bileaflet valves are usually preferred for their hemodynamic features, similar to physiological ones, and their durability, but they are prone to complications due to thromboembolic events. Due to the asynchronous closure of the leaflets, bileaflet MHVs are also known to produce closing sounds typically characterized by the presence of two peaks in the time domain. The detection of this "double click" in the signal may be useful for the early diagnosis of bileaflet MHV malfunction. The closing sound is actually a non-stationary signal that can be properly explored by means of time-frequency analysis. This paper describes a preliminary approach to the investigation of bileaflet MHV closing sounds performed by Continuous Wavelet Transform (CWT) analysis. Signals were collected from 3 patients immediately after surgery by means of the Myotis 3C, which is a traditional phonocardiographic apparatus. Signals were analyzed by two algorithms: one embedded in the Myotis 3C, based on the Fast Fourier Transform (FFT); and one specifically created for the purposes of the present study, based on CWT. The performance of these algorithms was compared and the results showed that the proposed CWT technique correctly classifies as ''double'' a large number of clicks that are recognized as ''single'' by the Myotis 3C.

Induction motors (IMs) are the workhorse of the industry and are subjected to a harsh environment. Due to their operating conditions, they are exposed to different kinds of unavoidable faults that lead to unscheduled downtimes and losses. These faults may be detected early through predictive maintenance (i.e., deployment of condition monitoring systems). Motor current signature analysis (MCSA) is the most widely used technique to detect various faults in industrial motors. The stator winding faults (SWF) are one of the major faults. In this paper, we present an induction motor fault detection and identification system using signal processing techniques such as fast Fourier transform (FFT), short-time Fourier transform (STFT), and continuous wavelet transform (CWT). A three-phase motor model is developed in MATLAB Simulink and simulated under various fault conditions. The current signature is observed using FFT, spectrogram, and scalogram to detect the faults. It is observed that under some fault conditions, the current signature analysis remains indistinguishable from the non-fault case. Therefore, deep learning (DL) methods are adopted here to identify these faults. The time-series data of healthy and unhealthy conditions are obtained from the simulation results. The comparative investigation among DL models confirmed the superiority of the long short-term memory (LSTM) model, which achieved 97.87% accuracy in identifying the individual faults.

In wind energy systems, doubly-fed induction generators (DFIGs) are widely used because they can produce electricity efficiently and operate over a wide range of wind speeds. However, like all electromechanical systems, DFIGs are prone to failures, one of which is open phase failure. The main objective of this paper is to present new results in the DFIG diagnostic approach for identifying stator and rotor open-phase failures. The approach is based on steady-state stator current analysis, using Fast Fourier Transform (FFT) and wavelets transforms (Continuous Wavelet Transform (CWT) and Discrete Wavelet Transform (DWT)) analysis with 2-D and 3-D approaches respectively. The effectiveness of the wavelet transform is confirmed by exposing simulation results, which demonstrate its ability to effectively analyze signals across various scales and resolutions. These results highlight how the wavelet transform can overcome traditional limitations associated with other signal processing techniques, such as the inability to provide localized information in both time and frequency domains. This capability is particularly evident in the 3-D time-frequency plot, where the wavelet transform offers a detailed and intuitive representation of the current signal. By capturing transient features and variations in the signal, the wavelet transform allows for a more comprehensive understanding of its underlying characteristics. Consequently, this method proves invaluable in applications such as audio processing, image analysis, and biomedical signal interpretation, where precise localization of features is crucial for accurate analysis and interpretation.

The Persian Gulf and its coastal areas are recognized as one of the biggest hydrocarbon basins in the world as world's largest petroleum reservoirs are located through its offshore and onshore oil and gas fields. Coastline countries of the Persian Gulf produce about 25% of the world's oil yearly and they have nearly two-thirds and one-third of the world's crude oil and natural gas reserves, respectively. In the Persian Gulf and south of Iran, Zagros orogeny process has a most important structural role as it causes many petroleum reservoirs into folds with northwest-southeast trends that are parallel with Zagros orogeny direction. However, there is good potential to explore new petroleum reservoirs in the Persian Gulf yet. One of these potential oilfields located northwestern of the Persian Gulf includes high petroleum potential, but with structural complexity and this investigation is focused to explore reservoir in its other horizons, specially Sarvak formation as the famous reservoir in the area. To achieve essential information from reservoir and locating it, we applied two useful seismic methods. Authors considered different advantages of the fast Fourier transform (FFT) and the continuous wavelet transform (CWT) as the most commonly applicable spectral analysis of seismic methods in an experimental investigation besides geological new findings. We found that the FFT can provide a good image from reservoir stratigraphic characteristics; it has specifically proven efficient even in carbonate reservoirs allowing individualization of geological bodies not easily defined in amplitude maps. Besides that, the CWT can provide an accurate and clear image from reservoir structural characteristics and low frequency shadows under petroleum reservoirs. We will prove our claims by using theoretical and experimental evidences. Objectives of this paper, beside geological evidences, are to show abilities of these two methods and to describes how, (1) the FFT method shows the distribution of the hidden reef boundaries and (2) the CWT shows the probable presence of hydrocarbons in purpose structure much better than the original seismic data and others methods.

Channels are hydrocarbon prospective areas which are often below the resolution of seismic data. This study was therefore conducted with the aim of using spectral decomposition methods for imaging of buried channels and associated structures in a 3D Post-Stack Depth Migrated (PSDM) volume acquired from a field in the Niger Delta Basin. Two commonly used spectral decomposition methods were used to enhance the resolution of seismic data for interpretation. The methods utilized included Fast Fourier Transform (FFT) and Continuous Wavelet Transform (CWT). Petrel and Opendtect were the interpretational software tools utilized for the study. The seismic data was conditioned using structural smoothing, and a zone of interest was selected around -1000 to -3000ms. Three dominant frequencies were selected from the sub-volume generated around the zone of interest. The frequencies were 10Hz, 25Hz and 32Hz respectively. These frequencies were extracted from the seismic data using FFT and CWT decomposition methods. The results were colored using Red, Green and Blue (Red for 10Hz, Green for 25Hz and Blue for 32Hz). These frequencies were then blended together in a process called RGB blending. The resultant output was a mix of only these three dominant frequencies. Analysis of these results revealed the presence of several channels, crevasse splay deposits, flood-plains and faults on two time-slices obtained at -2020ms and -1800ms. The channels were meandering channels of low sinuosity, some of which were fault controlled. The crevasse splay deposits were significantly large and increased in number at the shallow time-slice. Some of the crevasse splay deposits were found bifurcating fault lines and being deposited on floodplains, indicating that they were younger than the faults. Channel flow direction was from East to West, while channel migration was from South to North of the study area. The increase in the number of channels from the base to the top of the seismic data suggested a multistory stacked channel system. It was established that channels and crevasse splays were best enhanced using the FFT decomposition method while major and minor faults were best enhanced using CWT method. Hence, this study has proven that the spectral decomposition method is very effective in imaging subsurface buried channels, thus delineating prospects and can be used for reservoir characterization. Keywords: Spectral decomposition, Fast Fourier Transform (FFT), Continuous Wavelet Transform (CWT), Channels, Crevasse splays, Faults, Reservoir Characterization.

Fourier and wavelet analyses for fatigue assessment of concrete beams

Optical coherence tomography (OCT) imaging systems can now produce MB=s to GB=s data streams. We present a complete solution for signal acquisition up to 4 GS/s and on-board field programmable gate array (FPGA) OCT processing matching the high acquisition speed. On-board OCT signal processing virtually eliminates the downstream signal processing and data throughput bottleneck. Complex filtering allows for windowing and dispersion compensation. Data is zero-padded when the number of samples is not a power of 2. The Fast Fourier Transform (FFT) engine can match the maximum acquisition speed when performing 4096-point FFTs. Output data can be linear amplitude or logarithmic and represented on several floating-point or integer precisions. This hardware solution comes with dedicated software and software development kit.

The process of automatic sleep stage scoring consists of two major parts: feature extraction and classification. Features are normally extracted from the polysomnographic recordings, mainly electroencephalograph (EEG) signals. The EEG is considered a non-stationary signal which increases the complexity of the detection of different waves in it. This work presents a new technique for automatic sleep stage scoring based on employing continuous wavelet transform (CWT) and linear discriminant analysis (LDA) using different mother wavelets to detect different waves embedded in the EEG signal. The use of different mother wavelets increases the ability to detect waves in the EEG signal. The extracted features were formed based on CWT time frequency entropy using three mother wavelets, and the classification was performed using the linear discriminant analysis. Thirty-two data sets from the MIT-BIH database were used to evaluate the performance of the proposed method. Features of a single EEG signal were extracted successfully based on the time frequency entropy using the continuous wavelet transform with three mother wavelets. The proposed method has shown to outperform the classification based on a CWT using a single mother wavelet. The accuracy was found to be 0.84, while the kappa coefficient was 0.78. This work has shown that wavelet time frequency entropy provides a powerful tool for feature extraction for the non-stationary EEG signal; the accuracy of the classification procedure improved when using multiple wavelets compared to the use of single wavelet time frequency entropy.

The Brain Computer Interface (BCI) is a technology that provides non-muscular communication channels to utilize the external devices. The signal from the brain is recorded, then classified. To classify, time-frequency features are frequently extracted using Continuous Wavelet Transform (CWT). However, the CWT is computationally heavy. This becomes the bottleneck of the real-time processing of BCI systems. We introduce a new method to solve the CWT using piecewise polynomials approximation over mother wavelets. The implementation shows that our method, piecewise polynomials based CWT (PCWT), is clearly better than the state of the art computation using the Fast Fourier Transform in the smaller buffer, which is preferable in the real-time systems. The proposed method can apply to other applications and should provide an effective approach to the real-time signal processing.

Detection of chipping in ceramic cutting inserts from workpiece profile during turning using fast Fourier transform (FFT) and continuous wavelet transform (CWT)

Online detection of amplitude modulation of motor-related EEG desynchronization using a lock-in amplifier: Comparison with a fast Fourier transform, a continuous wavelet transform, and an autoregressive algorithm

In field harvesting conditions, the non-stationary random vibration characteristics of the harvester are rarely considered, and the results of vibration frequency calculated by different time–frequency transformation methods are different. In this paper, the harvester’s vibration characteristics under the time-varying mass were studied, and the correlation between vibration frequency and modal frequency was analyzed. Firstly, under the conditions of time-varying mass (field harvesting conditions) and non-time-varying mass (empty running condition), the non-stationarity characteristics of vibration signals at 16 measurement points of a combined corn harvester frame were studied. Then, fast Fourier transform (FFT), short-time Fourier transform (STFT), and continuous wavelet transform (CWT) were used to calculate the vibration frequency distribution characteristics of the corn harvester. Finally, based on the EFDD (enhanced frequency domain decomposition) algorithm, the correlation between the primary vibration frequency and the operating mode frequency is studied. The results show that the mean, variance, and maximum difference of the vibration amplitude under harvesting conditions (mass time-varying system) are 0.10, 26.5, and 1.0, respectively, at different harvesting periods (0~10 s, 10~20 s, 20~30 s). The harvesting conditions’ vibration signals conform to the characteristics of non-stationary randomness. The FFT algorithm is used to obtain more dense vibration frequencies, while the frequencies based on STFT and CWT algorithms are sparse. The correlation between the FFT method and the EFDD algorithm is 0.98, and the correlation between the STFT, CWT, and the EFDD algorithm is 0.99 and 0.98. Therefore, the primary frequency of the STFT methods is closer to the modal frequency. Our research laid the foundation for further study and application of mass time-varying combined harvester system non-stationary random vibration modal frequency identification and vibration control.

With the increasing maturity of adaptive signal processing technology, signal interference caused during electronic communication signal processing has become increasingly prominent. Therefore, this paper proposes to use the analysis of signal periodic characteristics and interference characteristics as variables, and modify the update relationship of step length in traditional algorithms. This enables the improved adaptive filtering algorithm to maintain its fast adaptive characteristics and excellent adaptive interference performance even under low signal-to-noise ratio conditions, achieving good experimental results. It can effectively extract changes in the periodic characteristics of communication signals. The application of the variable step-size least-squares algorithm for tracking time-varying signals is explored, specifically by introducing changes in the adaptive forgetting factor during the update process. This allows the forgetting factor value to be more flexible and have a more appropriate numerical range, thereby further enhancing its interference suppression capability and numerical stability. Under the same signal-to-noise ratio conditions (5 dB), the convergence speed of the improved variable step-size least-squares algorithm increased by 67%, and the steady-state value decreased by 2.7 dB. Similarly, in the application scenario of improving the time-varying tracking of the recursive least squares algorithm, when the interference signal-to-noise ratio is 20 dB, the convergence time is only 17.8 ms. This paper analyzes how to effectively improve the signal processing capability and interference resistance performance in the electronic communication signal processing process, thereby enhancing signal processing quality and effectiveness.

Two different sinusoidal wavelength-scanning (SWS) interferometers with a SWS light source using a superluminescent laser diode are proposed for step-profile measurement and real-time distance measurement, respectively. An optical path difference (OPD) longer than a wavelength is measured from detection of sinusoidal phase- modulation amplitude Zb of the interference signal that is proportional to the OPD and the scanning width 2b. In step-profile measurement, if measurement error in the OPD obtained from Zb is smaller than a half wavelength, this measured value of the OPD is combined with a fractional value of the OPD obtained from the conventional phase of the interference signal. This combination enables us to measure the OPD longer than a wavelength with a high accuracy of a few nm. In real-time distance measurement, the amplitude Zb is kept at a specified constant value for changes of OPD by controlling the scanning width 2b of the wavelength with a feedback system. The amplitude Zb is detected by processing the interference signal with electric circuits in real-time. The value of b is easily controlled in the SWS light source, and an OPD longer than a wavelength is measured from the value of b with an accuracy of about a wavelength.© (1999) COPYRIGHT SPIE--The International Society for Optical Engineering. Downloading of the abstract is permitted for personal use only.

In this paper, five types of tissues, human enamel, human cortical bone, human trabecular bone, muscular tissue, and fatty tissue were imaged <i>ex vivo</i> using optical coherence tomography (OCT). The specimens were prepared in blocks of 5 x 5 x 3 mm (width x length x height). The OCT imaging system was a swept source OCT system operating at wavelengths ranging between 1250 nm and 1360 nm with an average power of 18 mW and a scan rate of 50 to 100 kHz. The imaging probe was placed on top of a 2 x 2 cm stabilizing device to maintain a standard distance from the samples. Ten image samples from each type of tissue were obtained. To acquire images with minimum inhomogeneity, imaging was performed multiple times at different points. Based on the observed texture differences between OCT images of soft and hard tissues, spatial and spectral features were quantitatively extracted from the OCT images. The Radon transform from angles of 0 deg to 90 deg was computed, averaged over all the angles, normalized to peak at unity, and then fitted with Gaussian function. The mean absolute values of the spatial frequency components of the OCT image were considered as a feature, where 2-D fast Fourier transform (FFT) was done to OCT images. These OCT features can reliably differentiate between a range of hard and soft tissues, and could be extremely valuable in assisting dentists for <i>in vivo</i> evaluation of oral tissues and early detection of pathologic changes in tissues.